The height BH of the parallelogram ABCD divides its side AD into segments AH = 1 and HD = 63. The diagonal of the parallelogram BD is 65. Find the area of the parallelogram
Consider the triangle BDH.
This triangle is right-angled; therefore, we can apply the Pythagorean theorem:
BD2 = HD2 + BH2
65 ^ 2 = 63 ^ 2 + BH ^ 2
4225 = 3969 + BH ^ 2
BH ^ 2 = 256
Bh = 16
Find the area of the parallelogram:
S = AD * BH = (AH + HD) * BH = (1 + 63) * 16 = 1024
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